For a given frequency distribution,$\bar{x} = 19.7$,$A = 20$,and $n = 50$. Then,$\Sigma f_{i} d_{i} = \ldots$

While computing the mean of grouped data,we assume that the frequencies are

In the formula $\bar{x} = A + \frac{\Sigma f_{i} d_{i}}{\Sigma f_{i}}$,$d_{i} =$ .........

The mean of the following frequency distribution is $46$. Find the missing frequency $f$.

Class	$0-20, 20-40, 40-60, 60-80, 80-100, 100-120$
Frequency	$10, f, 7, 6, 5, 4$

The marks obtained by $30$ students of Class $X$ of a certain school in a Mathematics paper consisting of $100$ marks are presented in the table below. Find the mean of the marks obtained by the students.

Marks obtained $(x_{i})$	$10, 20, 36, 40, 50, 56, 60, 70, 72, 80, 88, 92, 95$
Number of students $(f_{i})$	$1, 1, 3, 4, 3, 2, 4, 4, 1, 1, 2, 3, 1$

Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarized as follows. Find the mean heartbeats per minute for these women,choosing a suitable method.

Number of heartbeats per minute	$65$-$68$	$68$-$71$	$71$-$74$	$74$-$77$	$77$-$80$	$80$-$83$	$83$-$86$
Number of women	$2$	$4$	$3$	$8$	$7$	$4$	$2$